Properties of Nonlinear Transformations of Fractionally Integrated Processes

Journal of Econometrics, Vol. 110, No. 2, pp. 113-133, 2002

UCSD Economics Discussion Paper No. 2000-07

25 Pages Posted: 1 Dec 2000 Last revised: 7 Aug 2009

See all articles by Ingolf Dittmann

Ingolf Dittmann

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE); Tinbergen Institute; Erasmus Research Institute of Management (ERIM); European Corporate Governance Institute (ECGI)

Clive W. J. Granger

University of California, San Diego (UCSD) - Department of Economics; Tinbergen Institute

Date Written: June 5, 2001

Abstract

This paper shows that the properties of nonlinear transformations of a fractionally integrated process depend strongly on whether the initial series is stationary or not. Transforming a stationary Gaussian I(d) process with d > 0 leads to a long-memory process with the same or a smaller long-memory parameter depending on the Hermite rank of the transformation. Any nonlinear transformation of an antipersistent Gaussian I(d) process is I(0). For non-stationary I(d) processes, every integer power transformation is non-stationary and exhibits a deterministic trend in mean and in variance. In particular, the square of a non-stationary Gaussian I(d) process still has long memory with parameter d, whereas the square of a stationary Gaussian I(d) process shows less dependence than the initial process. Simulation results for other transformations are also discussed.

Keywords: Nonlinear Transformations, Long Memory, Fractional Integration, Antipersistence, Nonstationarity, Hermite Rank, Moments

JEL Classification: C22

Suggested Citation

Dittmann, Ingolf and Granger, Clive W. J., Properties of Nonlinear Transformations of Fractionally Integrated Processes (June 5, 2001). Journal of Econometrics, Vol. 110, No. 2, pp. 113-133, 2002, UCSD Economics Discussion Paper No. 2000-07, Available at SSRN: https://ssrn.com/abstract=237008 or http://dx.doi.org/10.2139/ssrn.237008

Ingolf Dittmann (Contact Author)

Erasmus University Rotterdam (EUR) - Erasmus School of Economics (ESE) ( email )

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Clive W. J. Granger

University of California, San Diego (UCSD) - Department of Economics ( email )

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